We present the discovery of four new transiting hot Jupiters, detected mainly from SuperWASP-North and SOPHIE observations. These new planets, WASP-52b, WASP-58b, WASP-59b, and WASP-60b, have orbital periods ranging from 1.7 to 7.9 days, masses between 0.46 and 0.94 MJup, and radii between 0.73 and 1.49 RJup. Their G1 to K5 dwarf host stars have V magnitudes in the range 11.7−13.0. The depths of the transits are between 0.6 and 2.7%, depending on the target. With their large radii, WASP-52b and WASP-58b are new cases of low-density, inflated planets, whereas WASP-59b is likely to have a large, dense core. WASP-60 shows shallow transits. In the case of WASP-52 we also detected the Rossiter-McLaughlin anomaly via time-resolved spectroscopy of a transit. We measured the sky-projected obliquity λ = 24° +17-9, indicating that WASP-52b orbits in the same direction as its host star isrotating and that this prograde orbit is slightly misaligned with the stellar equator. These four new planetary systems increase our statistics on hot Jupiters and provide new targets for follow-up studies.